These are three distinct, but related disorders, and it has remained unclear how different or how similar they are. That can be important, as treatments differ.
PTSD shares most of its symptoms (fear reactions, avoidance, hypervigilance) with Complex PTSD, but the latter also shows emotional dysregulation, poor self-concept and problems in relationships.
BPD (or EUPD) can look very similar to Complex PTSD, but has a few extra symptoms: frantic attempts to avoid being abandoned, unstable relationships, unstable sense of self (the person with Complex PTSD has a consistent negative self-view), impulsiveness, self-harm, suicidality, chronic feelings of emptiness, anger issues and – usually brief – episodes of paranoid ideas and/or dissociation.
The one feature all three have in common is the central role of traumas and in that sense they may be understood as being on a spectrum. To put it in simple terms: an isolated – perhaps a one-off – severe trauma can lead to PTSD, but if the traumatic experience is chronic and not just a one-off, it can lead to Complex PTSD. If these persistent traumatic experiences occur when someone is young, their maturing personality gets damaged and that leads to BPD. It should be noted that there is not just a lot of overlap in symptoms: a lot of individuals have more than one of these three disorders: a researcher (Pagura) found in 2010 that 24% of individuals with PTSD also met criteria for BPD and 3% of people with BPD also had PTSD, whilst the same occurs in varying degrees with these two disorders and c-PTSD.
Another distinguishing feature is that for PTSD and c-PTSD there must be evidence of trauma, whereas someone can have BPD without any trauma being evident.
There is a clear difference in treatment approaches: for PTSD and c-PTSD treatment focuses on the traumatic experience and tries to ameliorate the traumatic memory. For BPD treatment is aimed at alleviating the emotional dysregulation and tendency to self-harm and to work on establishing a more consistent sense of self and of others, so that the relationships to self and others become more stable. For all three disorders both medication and various types of psychotherapy are used and often in combination, as most research points to better results if these combined treatment strategies are used.